Separating the inner conductors from the braid of shielded wire is one of those things that few people do cleanly and no one enjoys.  Even many experienced techs end up with a rather ugly mess if more than a half-inch of braid needs to be separated.  Here is a technique that is forehead-slapping obvious yet I was an electronics tech for many years and worked with dozens of other techs before I ever encountered it.

You will need a pointed instrument.  A dentist's pick works great.  A straightened paper clip can be used in a pinch.  Avoid using a knife point as it is likely that you will end up cutting some of the fine strands of wire.

1. Strip the outer insulation from the shielded cable.  Be very careful not to cut any of the fine strands of wire that make up the shielding braid.
   
   
   
   
   
   
   
2. Using a pointed instrument carefully "pick" a hole in the braid.  Be careful not to cut or break any of the fine strands of wire, just form a hole in the weave of the braid by pushing the strands aside.
   
   
   
   
   
   
3. Bend the cable sharply where you picked the hole in the braid.  Make sure that the hole is facing away from the bend.  Use your dental pick or similar instrument to work a loop of the inner conductor(s) out through the hole in the braid.
   
   
   
   
   
4. Keep pulling on the loop of inner conductor until the loose end comes completely free of the braid.
   
   
   
   
   
   
   
   
5. When tinning or soldering the braid, use a heatsink right at the hole to prevent the hot braid from melting the insulation on the inner conductor(s).  Surgical hemostats (yeah, the ones you wore around your neck in the 70's) make a great heat sink.